Let’s describe the population and LICO-AT by DA:

Median number of care destinations spatially accessible (by walk) within 15 mins from a parcel in each DA:

We will focus on the following DAs based on our discussion 10 June.

How did we decide these DAs? We pick the highest and highest DA in LOWER-Hamilton Central and MOUNTAIN-Hamilton Central that contain care destinations. We then picked three more DAs with similar values neighbouring the selected DA. The following 3 plots showcase these selected DAs.

Let’s see the accessibility, population and LICO for just these DAs (NOTE: click on the DA to see the accessibility, population and LICO-AT values:

OSM Street network with the posted vehicle speeds within 400m buffers around destinations per DA:

*CAUTION WHEN USING SPEEDS FROM THIS MAP. I believe what’s displayed is the whole segment average speed. I’m displaying the road network as used by {r5r} and I can only speculate that it averages the road segment speed to increase computational efficiency. However, in real life, the posted speed varies within parts of each segment. So it would be worth double-check speeds that do not end in 0s in the field / google street view. I’m not certain how to display the OSM road network as-is (unaveraged speeds), and it may not be worth my time figuring out at this point. But let me know!

AN ALTERNATIVE APPROACH - LISA methods

What we’re trying to do is determine high and low clusters - this is spatial autocorrelation! Spatial autocorrelation refers to the extent to which a variable is correlated with itself through space. Think “everything is related to everything else, but near things are more related than distant things” (Tobler 1970). Positive spatial autocorrelation indicates that observations are very similar in values (i.e., spatially clustered). Negative spatial autocorrelation occurs when observations with dissimilar values are closer together (i.e., spatially dispersed).

Moran’s I statistic can be calculated to describe spatial autocorrelation.

For the whole City of Hamilton, we calculate a positive spatial autocorrelation:

## 
##  Moran I test under randomisation
## 
## data:  access_15_DA$med_copp_isc  
## weights: nbw    
## 
## Moran I statistic standard deviate = 46.805, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      0.9143959155     -0.0011273957      0.0003826132

Moran’s I statistic is 0.9143959, very close to 1 (i.e., positive spatial autocorrelation), with a p-value of lower than 0.05 indicating significance. We can reject the null hypothesis and conclude there is evidence for positive spatial autocorrelation for the whole region. Positive spatial autocorrelation indicates that neighbours are very similar in values. This can be clusters of high values, and clusters of low values.

But where are the clusters? We can calculate the local Moran’s I – this involves tabulating the spatial moving average for each DA (the average value of all the neighbours around each DA, for each DA). Let’s only focus on the Hamilton Central area (I did this analysis for the rest of Hamilton, and it only has concentrations of low-low).

The closer the points are to the vertical line – the more spatially autocorrelated the dataset is. Let’s spatially visualise the statistically significant results where the top right quadrant of the plot above is (high-high) and the bottom left quadrant is (low-low) values:

Now let’s plot the accessibility values for only DAs that have statistically signficant quadrant 1 (high-high) and quadrant 2 (low-low) values:

The black outlines are the ‘selected’ clusters from our conversation June 10, with an alternative low option in LOWER - HAMILTON CENTRAL.

It can be seen that only the selected LOW-HAMILTON CENTRAL higher cluster and the MOUNTAIN-HAMILTON CENTRAL lower cluster overlap the Local Moran’s I clusters.

How do we interpret the Local Moran’s I clusters? An advantage is it yields a statistical significance value. In the DAs that are shown in the map above, the are either high-high clusters or low-low clusters. A high-high cluster are DAs that have accessibility values that are high and are surrounded by neighbours that are relatively high in a statistically significant way; meaning, that if the values of Hamilton Central were shuffled and randomly assigned to DAs (i.e., a random ’null hypothesis), the chance of these clusters occurring are less than 0.05%. Same goes for the low-low clusters. Moran’s I is a common statistic used in spatial analysis.

The issue here is – there is no high-high cluster in MOUNTAIN-HAMILTON CENTRAL. In fact, there is a high-high cluster in LOWER - HAMILTON CENTRAL – no where else in the City of Hamilton.

We can also try another “Local Statistics of Spatial Association” (LISA) approach to detect clusters – the \(G^*\) statistic (Getis and Ord, 1992). In this measure, the spatial weights are not row-standardized and are binary. In the Local Moran’s I we calculated the weighted spatial moving average. In this measure, we instead calculate the total of the variable in the neighborhood (i.e., being the value of the DA and the value of all the DAs touching a DA).

We see from the map above, the result is quite similar as the Local Moran’s I map. Why? I think because positive spatial autocorrelation is quite apparent and what we define as a neighbour is quite similar (i.e., a neighbour for each DAs are the DAs that border it). Is this a good way of defining a neighbourhood? Not sure. We don’t have information on what is a good distance away from a DA to be considered within the same neighbourhood (i.e., no surveys of people’s perceptions). So once again, stats are complex and shed a some light but leave other things unknown. Thought it was worthwhile adding in these methods as food for thought.